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Forum: And now for something completely different 2021-09-27, 05:55
Replies: 10
Views: 855
Posted By Alfred
I informed Makoto Kamada. Thank you.

I informed Makoto Kamada.



Thank you.
Forum: Puzzles 2021-08-11, 18:01
Replies: 8
Views: 1,771
Posted By Alfred
Is it possible to "compute" p2*p3-1 as smallest...

Is it possible to "compute" p2*p3-1 as smallest and n-(p2*p3-1) as largest non-trivial root?
Forum: And now for something completely different 2021-06-08, 11:23
Replies: 10
Views: 855
Posted By Alfred
Any other in the specified range is meant.

Any other in the specified range is meant.
Forum: And now for something completely different 2021-06-08, 07:20
Replies: 10
Views: 855
Posted By Alfred
10^n+7: four PRPs

I've found four probable primes in the range 200001 <= n <= 500000:

n = 221628, 350071, 371696, 487291.

IMO any other 10^n+7 is composite.

The attached file should "prove" this assertion.
Forum: Factoring 2021-04-15, 18:00
Replies: 36
Views: 9,052
Posted By Alfred
Largest 10^n - c with exactly five equally sized prime factors, part 3

The solutions for n = 46, 47, 48, 49 are as follows.

n c p q r s t
======================================================================
49 ...
Forum: Factoring 2021-03-24, 09:13
Replies: 36
Views: 9,052
Posted By Alfred
Largest 10^n - c with exactly five equally sized prime factors, part 2

The solutions for n = 42, 43, 44 are as follows.


n c p q r s t
======================================================================
44...
Forum: Factoring 2021-02-13, 09:34
Replies: 36
Views: 9,052
Posted By Alfred
The Big Four

I've found the largest four 67-digit numbers with exactly four equally sized prime factors.

In 10^67 - c representation:


c p q r ...
Forum: And now for something completely different 2021-02-03, 20:51
Replies: 80
Views: 25,583
Posted By Alfred
Thank you - for your congrats and your correct...

Thank you - for your congrats and your correct attribution.
Forum: Factoring 2021-01-22, 09:28
Replies: 36
Views: 9,052
Posted By Alfred
Largest 10^n - c with exactly five equally sized prime factors

The solutions for some smaller n are as follows.


n c p q r s t
======================================================================
41 ...
Forum: Factoring 2020-12-26, 11:27
Replies: 36
Views: 9,052
Posted By Alfred
But it does not. The file contains 282 lines,...

But it does not.
The file contains 282 lines, where the smallest primefactor has 31 digits.
For these numbers the attached file shows that the remaining cofactor is a 61-digit prime.

Now the...
Forum: Factoring 2020-12-24, 14:36
Replies: 36
Views: 9,052
Posted By Alfred
10^91-1250741 is 3-brilliant

10^91 - 1250741
1130907742078987214643014936029
2064984395278432435681546498733
4282092540978287980470405630787

There is no larger 91-digit number which splits into three equally sized prime...
Forum: Factoring 2020-12-21, 08:26
Replies: 36
Views: 9,052
Posted By Alfred
I'd like to take 10^201 - c.

I'd like to take 10^201 - c.
Forum: Factoring 2020-12-03, 11:50
Replies: 36
Views: 9,052
Posted By Alfred
What is the worthy cause of this outstanding...

What is the worthy cause of this outstanding observation?
Forum: Factoring 2020-11-27, 09:16
Replies: 36
Views: 9,052
Posted By Alfred
10^157 - 2049 is brilliant

10^157 - 2049 is the largest 157-digit number with two 79-digit prime factors.


10^157 - 2049
1446814727739974723827555617027876206977909532017942734175294759323847644834853...
Forum: Factoring 2020-11-21, 16:06
Replies: 525
Views: 101,941
Posted By Alfred
p54 with ecm and B1 = 3e6

Caught this p54 while searching for a brilliant 199-digit number.

Input number is...
Forum: Factoring 2020-11-21, 15:56
Replies: 36
Views: 9,052
Posted By Alfred
Largest c199, splitting as p100 * q100

After a longer search, starting in September (!), I found this factorization:


10^199 - 5399 =
16656894422236107849246117001467083363915297020262\...
Forum: Factoring 2020-11-20, 07:29
Replies: 36
Views: 9,052
Posted By Alfred
10^199-c

I'd like to continue with these numbers.
It will take a while.
Forum: Factoring 2020-11-01, 18:42
Replies: 49
Views: 24,467
Posted By Alfred
I think it is a good idea to share these...

I think it is a good idea to share these informations.

Thank you.

So anyone who is interested in can doublecheck the

correctness of the statements easily.
Forum: Factoring 2020-10-15, 14:46
Replies: 36
Views: 9,052
Posted By Alfred
Largest 10^86 - c 3-Brilliant Number (p29 * p29 * p29)

10^86 - 2007389 is the largest 86-digit number with three 29-digit prime factors.

The appended file proves this.

Any line (except the last one) has exactly two entries.

The first shows c.
...
Forum: Factoring 2020-10-14, 13:59
Replies: 49
Views: 24,467
Posted By Alfred
Dr Sardonicus, thank you for your...

Dr Sardonicus,

thank you for your explanation.
Forum: Factoring 2020-10-14, 08:54
Replies: 49
Views: 24,467
Posted By Alfred
Dr Sardonicus, does this statement apply to...

Dr Sardonicus,

does this statement apply to largest 2-brilliant numbers in base 10?

If yes, please give an example.
Forum: Factoring 2020-10-06, 20:32
Replies: 36
Views: 9,052
Posted By Alfred
Largest 10^153-c Brilliant Number (p77*p77)

No 10^153-c with c>0 smaller than 24783 splits as p77*p77.

The attached file shows the smallest prime factor
for any of these c's - or it indicates that 10^153-c is prime.
...
Forum: Factoring 2020-09-30, 06:18
Replies: 36
Views: 9,052
Posted By Alfred
Yes, of course. Thank you for your information....

Yes, of course.
Thank you for your information.

I'd like to take the numbers 10^153-c.
Forum: Factoring 2020-09-29, 07:01
Replies: 36
Views: 9,052
Posted By Alfred
Largest 10^151-c Brilliant Number (p76*p76)

No 10^151-c with c>0 smaller than 13731 splits as p76*p76.

The attached file shows one factor (prime or composite but with less digits)
for any of these c's - or it indicates that 10^151-c is...
Forum: Factoring 2020-09-26, 07:55
Replies: 36
Views: 9,052
Posted By Alfred
Largest 10^147-c Brilliant Number (p74*p74)

No 10^147-c with c>0 smaller than 28239 splits as p74*p74.

The attached file shows one factor (prime or composite but with less digits)
for any of these c's - or it indicates that 10^147-c is...
Showing results 1 to 25 of 87

 
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